assign2_electrostatics

assign2_electrostatics - L1 =2k C/m and L2 =-2k C/m passing...

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EE1259: Electromagnetic assignment 1 EE1259 Assignment 3 ((Due on 9:30am, October 10, 2006) 1. The electric flux density inside a dielectric sphere of radius a centered at the origin is given by r a r D r 0 ρ = (C/m 2 ) Apply Gauss’s law to find charge density . 2. If the charge density increases linearly with distance from the origin such that v =10 C/m 3 at r=2m , find the corresponding variation of D . 3. Given that otherwise m nC v ) 2 1 ( 0 / 12 3 < < = Determine D r everywhere 4. For a spherical charge distribution > < = a r a r r a v 0 2 2 0 ) ( a. Determine E r everywhere b. Find the total charge c. Find the location with maximum E r 5. Point charges Q and –Q are located at (0, d/2,0), and (0, -d/2, 0). Show that at point ( r, θ , φ ), where r>>d 2 0 4 r Qd V πε sin sin = Also, find the corresponding E r field 6. A sphere of radius a and dielectric constant ε r has a uniform charge density 0 , show that a. At the center of the sphere: () 1 2 6 0 0 + = r r a V b. Find the potential at the surface of the sphere. 7. Show that for two infinitely long line charges parallel to the z-axis, having uniform densities
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Unformatted text preview: L1 =2k C/m and L2 =-2k C/m passing through (-1,0,0) and (1,0,0), respectively, the potential is given by ( ) ( ) k r r r r V 1 2 2 1 / ln , = Where r 2 and r 1 are distances to the point from the line charges 1 and 2, respectively. 8. A volume charge distribution is given in spherical coordinates by > < = a r for a r for a r ) / ( 2 (a). Find the work required to re-arrange the charge with uniform density within the region (r<a). (b). Instead of as in part (a), find the radius of the spherical region and the charge density for which neither additional work is required nor work is made available in the redistributing the charge uniformly within the region. EE1259: Electromagnetic assignment 2...
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This note was uploaded on 04/10/2008 for the course ECE 1259 taught by Professor Chen during the Spring '07 term at Pittsburgh.

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assign2_electrostatics - L1 =2k C/m and L2 =-2k C/m passing...

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